A vehicle-following control, which is a known vehicle cruise-assist control, causes the own vehicle to follow a preceding vehicle that travels on the same lane as the own vehicle among preceding vehicles traveling ahead of the own vehicle. In such vehicle-following control, for example, it is important that a vehicle traveling on the same lane as the own vehicle is identified with high accuracy among the preceding vehicles detected by, for example, a sensor or a camera. For this reason, a preceding vehicle present on a computed future course of the own vehicle is conventionally used as a target of the vehicle-following control. There are various methods of calculating a future course of the own vehicle (see, for example, PTL 1). The method disclosed in PTL 1 involves storing the trajectory of a vehicle traveling ahead of the own vehicle and, based on the stored trajectory, calculating a future course of the own vehicle.